Question: Ted likes to run long distances. He can run $20 \text{ km}$ in $95$ minutes. He wants to know how many kilometers $(k)$ he will go if he runs at the same pace for $285$ minutes. How far will Ted run in $285$ minutes?
We're dealing with a proportional relationship, so each ratio of kilometers to minutes must be equivalent. We can set up a proportion like this: $\dfrac{20 \text{ km}}{95 \text{ minutes}}=\dfrac{k \text{ km}}{285 \text{ minutes}}$ We can solve for $k$ by isolating it. $k \text{ km}=\dfrac{20 \text{ km}}{95 \cancel{\text{ minutes}}}\cdot285 \cancel{\text{ minutes}}$ $\begin{aligned} k&=\dfrac{20}{95}\cdot 285 \\\\ &=\dfrac{20}{\cancel{95}}\cdot(\cancel{95}\cdot3) \\\\ &=20\cdot3 \\\\ &=60 \end{aligned}$ Ted will run $60\text{ km}$ in $285$ minutes.